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\text{已知}$f\left( x\right) $\text{可导，且}$\left| f'\left( x\right) \right| \leq \dfrac{1}{e}$\text{，方程}$f\left( x\right) =x$\text{有唯一解}$x=0$\text{，又}$x_{n+1}=f\left( x_{n}\right) ,n=1,2,\ldots $\text{.证明：当}$n\rightarrow \infty $\text{时，}$x_{n}$\text{是}$e^{-\frac{n}{2}}$\text{的高阶无穷小.}
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